Solve 9sqrt{45}+2sqrt{20}

$$9 \sqrt { 45 } + 2 \sqrt { 20 }$$

Evaluate

$$31\sqrt{5}\approx 69.318107302$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$9\times 3\sqrt{5}+2\sqrt{20}$$

Multiply 9 and 3 to get 27.

$$27\sqrt{5}+2\sqrt{20}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$27\sqrt{5}+2\times 2\sqrt{5}$$

Multiply 2 and 2 to get 4.

$$27\sqrt{5}+4\sqrt{5}$$

Combine 27\sqrt{5} and 4\sqrt{5} to get 31\sqrt{5}.

$$31\sqrt{5}$$